Question

In order to cover a fixed distance of 48 km, two vehicles start from the same place. The faster one takes 2 hrs less and has a speed 4 km/hr more than the slower one. What is the speed (in km/hr) of the slower vehicle?​

Answer 1

Question :-

• In order to cover a fixed distance of 48 km, two vehicles start from the same place. The faster one takes 2 hrs less and has a speed 4 km/hr more than the slower one. What is the speed (in km/hr) of the slower vehicle?

Answer

Given :-

• Distance covered = 48 km
• The speed of one vehicle is 4 km/hr more than the other vehice.
• Time taken by fast vehicle is 2 hours less than slower one.

To find :-

• Speed of the slower vehicle.

Formula used :-

$\bf \:Time = \dfrac{Distance}{Speed}$

★ Solution :-

Let assume that speed of slower vehicle be 'x' km/hr.

So, speed of fast vehicle is (x + 4) km/hr.

★ Case 1 :-

Distance to be covered = 48 km

Speed of slower vehicle = x km/hr.

So, time taken to covered 48 km is

$\bf\implies \:t_1 = \dfrac{48}{x} \: hours$

★ Case 2 :-

Distance to be covered = 48 km

Speed of faster vehicle = (x + 4) km/hr.

So, time taken to covered 48 km is

$\bf\implies \:t_2 = \dfrac{48}{x + 4}$

★ According to statement,

Time taken by fast vehicle is 2 hours less than slower one.

$\bf\implies \:t_1 - t_2 = 2$

$\bf\implies \:\dfrac{48}{x} - \dfrac{48}{x + 4} = 2$

$\bf\implies \:48(\dfrac{1}{x} - \dfrac{1}{x + 4} ) = 2$

$\bf\implies \:48(\dfrac{x + 4 - x}{x(x + 4)} ) = 2$

$\bf\implies \:24 \times \dfrac{4}{ {x}^{2} + 4x} = 1$

$\bf\implies \: {x}^{2} + 4x - 96 = 0$

$\bf\implies \: {x}^{2} + 12x - 8x - 96 = 0$

$\bf\implies \: x(x + 12) - 8(x + 12) = 0$

$\bf\implies \:(x + 12)(x - 8) = 0$

$\bf\implies \:x = 8$

$\bf \:★ \: So, \: speed \: of \: slower \: vehicle = 8 \: km/hr.$

Answer 2

Answer:

this is correct........................